{
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  {
   "cell_type": "markdown",
   "metadata": {
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    "originalKey": "4bfb56b8-d8bc-4ba5-9ef5-456ba0f58ec4",
    "showInput": false
   },
   "source": [
    "# Tutorial: Maximum likelihood and maximum a priori point estimation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "customInput": null,
    "originalKey": "49a58523-6733-4675-a6de-48d14056cd64",
    "showInput": false
   },
   "source": [
    "This tutorial demonstrates how maximum likelihood estimation (MLE) and maximum a priori (MAP) inference problems\n",
    "can be specified and solved using Bean Machine's variational inference. MLE is treated as a special case of MAP where\n",
    "priors are uninformative, and MAP is treated as a special case of VI point estimation (i.e. with `Delta` guide distributions)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "customInput": null,
    "originalKey": "90f78439-adf5-4b54-82d5-05a2220b44b7",
    "showInput": false
   },
   "source": [
    "## Prerequisites"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Install Bean Machine in Colab if using Colab.\n",
    "import sys\n",
    "\n",
    "\n",
    "if \"google.colab\" in sys.modules and \"beanmachine\" not in sys.modules:\n",
    "    !pip install beanmachine"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import beanmachine.ppl as bm\n",
    "import matplotlib.pyplot as plt\n",
    "import torch\n",
    "import torch.distributions as dist\n",
    "from beanmachine.ppl.distributions import Flat\n",
    "from beanmachine.ppl.inference.vi import MAP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "\n",
    "# Plotting settings\n",
    "plt.rc(\"figure\", figsize=[8, 6])\n",
    "plt.rc(\"font\", size=14)\n",
    "plt.rc(\"lines\", linewidth=2.5)\n",
    "\n",
    "# Manual seed\n",
    "bm.seed(11)\n",
    "torch.manual_seed(11)\n",
    "\n",
    "# Other settings for the notebook.\n",
    "smoke_test = \"SANDCASTLE_NEXUS\" in os.environ or \"CI\" in os.environ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "customInput": null,
    "originalKey": "16e332f0-da5b-430b-a8dc-7b6dac9c4422",
    "showInput": false,
    "tags": []
   },
   "source": [
    "## Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "code_folding": [],
    "customInput": null,
    "executionStartTime": 1651183071627,
    "executionStopTime": 1651183072762,
    "hidden_ranges": [],
    "originalKey": "3b58af7f-370a-46ac-af55-f4f21e542f06",
    "requestMsgId": "3b58af7f-370a-46ac-af55-f4f21e542f06",
    "showInput": false
   },
   "source": [
    "Consider data following the OLS model $Y \\sim N([X; 1]^\\top \\beta_{\\text{true}}, 1.0)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": {
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       "bar_format": null,
       "colour": null,
       "elapsed": 0.04594993591308594,
       "initial": 0,
       "n": 0,
       "ncols": null,
       "nrows": 16,
       "postfix": null,
       "prefix": "Samples collected",
       "rate": null,
       "total": 1,
       "unit": "it",
       "unit_divisor": 1000,
       "unit_scale": false
      },
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "57495f285a5446f3b914bfa5a6ce01a2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Samples collected:   0%|          | 0/1 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x145765100>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 900\n",
    "true_beta = torch.tensor([2.0, 5.0])\n",
    "\n",
    "@bm.random_variable\n",
    "def X():\n",
    "    return dist.Normal(0, 1).expand((N,1))\n",
    "\n",
    "def beta():\n",
    "    return true_beta\n",
    "\n",
    "@bm.random_variable\n",
    "def Y():\n",
    "    return dist.Normal((torch.cat([X(), torch.ones((N,1))], dim=1) @ beta()).squeeze(), 1.0)\n",
    "\n",
    "data = bm.simulate([X(), Y()], num_samples=1).get_chain(0)\n",
    "data_X, data_Y = data[X()], data[Y()]\n",
    "xs = torch.linspace(-3, 3, steps=100)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(data_X, data_Y, label='data')\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "originalKey": "8c3155b7-e158-489c-9c40-770a6f26af95",
    "showInput": false
   },
   "source": [
    "## Maximum Likelihood Estimation (MLE)\n",
    "\n",
    "By placing a `Flat` uninformative prior over $\\beta$, the prior has no effect and the likelihood\n",
    "and posterior become equal. Therefore, we can use MAP to search for the MLE estimate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": {
       "ascii": false,
       "bar_format": null,
       "colour": null,
       "elapsed": 0.020793914794921875,
       "initial": 0,
       "n": 0,
       "ncols": null,
       "nrows": 16,
       "postfix": null,
       "prefix": "",
       "rate": null,
       "total": 1500,
       "unit": "it",
       "unit_divisor": 1000,
       "unit_scale": false
      },
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "992b281888324a1a889339b6a1c1aefb",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/1500 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[1.9999],\n",
      "        [4.9858]], requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "@bm.random_variable\n",
    "def beta():\n",
    "    return Flat(shape=(2,1))\n",
    "\n",
    "@bm.random_variable\n",
    "def Y():\n",
    "    return dist.Normal((torch.cat([X(), torch.ones((N,1))], dim=1) @ beta()).squeeze(), 1.0)\n",
    "\n",
    "\n",
    "v_world = MAP(\n",
    "    queries=[beta()],\n",
    "    observations={\n",
    "        X(): data_X,\n",
    "        Y(): data_Y,\n",
    "    },\n",
    ").infer(num_steps=1500)\n",
    "with v_world:\n",
    "    print(beta())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with v_world, torch.no_grad():\n",
    "    ax.plot(xs, torch.cat([xs.unsqueeze(1), torch.ones((len(xs),1))], dim=1) @ beta(), color='yellow', label='MLE')\n",
    "ax.legend()\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "customInput": null,
    "originalKey": "731a7e18-ceee-466e-855b-81d111ede201",
    "showInput": false
   },
   "source": [
    "`MAP` performs gradient descent on a quadratic potential centered at the standard OLS estimator,\n",
    "which is known to be given by the Moore-Penrose pseudo-inverse:\n",
    "$$\\hat\\beta_{OLS} = X^\\dagger y = (X^\\top X)^{-1} X^\\top y$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "customInput": null,
    "originalKey": "731a7e18-ceee-466e-855b-81d111ede201",
    "showInput": false
   },
   "source": [
    "`MAP` performs gradient descent on a quadratic potential centered at the standard OLS estimator,\n",
    "which is known to be given by the Moore-Penrose pseudo-inverse:\n",
    "$$\\hat\\beta_{OLS} = X^\\dagger y = (X^\\top X)^{-1} X^\\top y$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([2.0001, 5.0015])\n"
     ]
    }
   ],
   "source": [
    "beta_ols = torch.linalg.pinv(torch.cat([data_X, torch.ones((N,1))], dim=1)) @ data_Y\n",
    "print(beta_ols)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax.plot(xs, torch.cat([xs.unsqueeze(1), torch.ones((len(xs),1))], dim=1) @ beta_ols, color='red', label='OLS')\n",
    "ax.legend()\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "originalKey": "1faf4bcc-4839-4806-a493-25f8ccdb0ca4",
    "showInput": false
   },
   "source": [
    "## MAP Inference\n",
    "\n",
    "To incorporate prior beliefs, such as $\\beta \\sim N(0,\\tau)$ in this example,\n",
    "the `Flat` uninformative prior is replaced with a prior distribution that with\n",
    "high precision ($\\sigma = 0.1$ is small) assigns the majority of probability\n",
    "belief near zero. This prior results in a combined posterior which \"shrinks\" estimates\n",
    "away from the MLE and back towards the prior (in this case, both regression coefficients\n",
    "$\\beta_i$ are shrunken towards $0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/json": {
       "ascii": false,
       "bar_format": null,
       "colour": null,
       "elapsed": 0.016337871551513672,
       "initial": 0,
       "n": 0,
       "ncols": null,
       "nrows": 16,
       "postfix": null,
       "prefix": "",
       "rate": null,
       "total": 1000,
       "unit": "it",
       "unit_divisor": 1000,
       "unit_scale": false
      },
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b442db3520c143ddad4f97b6672d2e0e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/1000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[1.7862],\n",
      "        [4.4997]], requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "sigma = 0.1\n",
    "\n",
    "@bm.random_variable\n",
    "def beta():\n",
    "    return dist.Normal(0, sigma).expand((2,1))\n",
    "\n",
    "@bm.random_variable\n",
    "def Y():\n",
    "    return dist.Normal((torch.cat([X(), torch.ones((N,1))], dim=1) @ beta()).squeeze(), 1.0)\n",
    "\n",
    "v_world = MAP(\n",
    "    queries=[beta()],\n",
    "    observations={\n",
    "        X(): data_X,\n",
    "        Y(): data_Y,\n",
    "    },\n",
    ").infer(num_steps=1000)\n",
    "with v_world:\n",
    "    print(beta())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with v_world, torch.no_grad():\n",
    "    ax.plot(xs, torch.cat([xs.unsqueeze(1), torch.ones((len(xs),1))], dim=1) @ beta(), color='cyan', label='MAP')\n",
    "ax.legend()\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "customInput": null,
    "customOutput": null,
    "executionStartTime": 1661300362511,
    "executionStopTime": 1661300362587,
    "originalKey": "ccf6dbcc-9088-46a2-9274-22ab9d4473a3",
    "requestMsgId": "8b581749-fe8a-4a6f-a5b3-b7efccf077a2",
    "showInput": false
   },
   "source": [
    "It turns out some MAP estimates correspond to frequentist regularization techniques.\n",
    "In the case of linear regression, MAP inference with a Normal prior is equivalent to Tikhonov or $L_2$ regularization\n",
    "where the regularization parameters $\\lambda = \\sigma^{-2}$ the prior variance:\n",
    "$$\\hat{\\beta}_{L_2,\\lambda} = (X^\\top X + \\sigma^{-2} I)^{-1} X^\\top y$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([1.7862, 4.4998])\n"
     ]
    }
   ],
   "source": [
    "X_full = torch.cat([data_X, torch.ones((N,1))], dim=1)\n",
    "beta_l2 = (torch.linalg.inv(X_full.T @ X_full + sigma**-2 * torch.eye(2)) @ X_full.T @ data_Y)\n",
    "print(beta_l2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax.plot(xs, torch.cat([xs.unsqueeze(1), torch.ones((len(xs),1))], dim=1) @ beta_l2, color='magenta', label='L2')\n",
    "ax.legend()\n",
    "fig"
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "name": "python"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
